Math Exam VIII about Volume and Surface Area of Sphere, Cylinder, Cuboid, cube, cone, pyramid, and Hemisphere

Math Exam VIII

Volume and Surface Area of shape

I. Choose the correct answer by crossing the letter A, B, C, or D
1. A construction worker is on a ladder that is placed agains a vertical wall. Given
that the top of the ladder is (2x + 2) m above the ground and the foot of the
ladder is place (x – 4) m. The worker put the base of a (2x + 3) m foot ladder.
The length of the ladder is ….

A. 7m
B. 24 m
C. 25 m
D. 31 m

Answer: (2x + 3)2 = (2x + 2)2 + (x-4)2

X = 31 m




2. John puts the base of a 15 foot ladder 12 feet from the wall of his house. The
distance between the base of the wall to the top of the ladder is ….


A. 5 feet
B. 7.5 feet
C. 9 feet
D. 12 feet

Answer: H2 = 152 – 122
H2 = 225– 144
H = √81
H = 9 feet

, 3. Randy wants to attach a 39 foot string of lights to the top of the 36 foot mast of
his sailboat. The length of the base of the mast should he attach the end of the
light string is ….
A. 10 feet
B. 13 feet
C. 15 feet
D. 21 feet

Answer: B2 = 392 – 362
B2 = 1521 – 1296
B = √225
B = 15 feet



4. A ladder 13 m long is placed on the ground in such a way that it touches the top
of a vertical wall 12 m high. The distance of the foot of the ladder from the bottom
of the wall is ….


A. 3m
B. 4m
C. 5m
D. 6m

Answer: 𝑎2 − 𝑏 2 = 𝑐 2
132 − 122 = 𝑐 2
169 − 144 = 𝑐 2
√25 = 𝑐
5m=𝑐




5. A campsite in the shape of a rectangle ABCD has sides of length (p + 15) cm and
10 cm, and the length of the diagonal BD is (p + 17) cm.
The perimeter and the area of the rectangle are ….

A. 20 cm and 25 cm2
B. 42 cm and 255 cm2
C. 68 cm and 240 cm2
D. 112 cm and 325 cm2